# Dataplot Solution to the Non-Linear Fitting Problem

Problem Setup An analyst has a data set consisting of (x,y) pairs. Read the data into the computer. Plot them. Carry out a non-linear fit for the model
y = exp(-alpha*x)/(a+b*x)
Generate a superimposed plot of raw data and predicted values from the fit. Generate a plot of residuals versus x. Generate a normal probability plot of the residuals.
Dataplot Code This is demonstrated with the built-in data file CHWIRUT1.DAT (stored in the Dataplot auxiliary directory). The following Dataplot program
SKIP 25
TITLE AUTOMATIC
PLOT Y X
.
LET A = 0.01
LET B = 0.01
LET ALPHA = 0.1
FIT Y = EXP(-ALPHA*X)/(A+B*X)
.
CHARACTERS X BLANK
LINES BLANK SOLID
PLOT Y PRED VS X
PLOT RES X
NORMAL PROBABILITY PLOT RES
Plot of Raw Data generated the following output

Fit Output
```LEAST SQUARES NON-LINEAR FIT
SAMPLE SIZE N =      214
MODEL--Y =EXP(-ALPHA*X)/(A+B*X)
REPLICATION CASE
REPLICATION STANDARD DEVIATION =     0.3281762600D+01
REPLICATION DEGREES OF FREEDOM =         192
NUMBER OF DISTINCT SUBSETS     =          22

ITERATION  CONVERGENCE  RESIDUAL  *  PARAMETER
NUMBER      MEASURE    STANDARD  *  ESTIMATES
DEVIATION *
----------------------------------*-----------
1--  0.10000E-01  0.72640E+01 * 0.10000E+00 0.10000E-01 0.10000E-01
2--  0.50000E-02  0.40184E+01 * 0.12438E+00 0.41130E-02 0.13518E-01
3--  0.25000E-02  0.33689E+01 * 0.18239E+00 0.60968E-02 0.10633E-01
4--  0.12500E-02  0.33617E+01 * 0.18967E+00 0.61251E-02 0.10549E-01

FINAL PARAMETER ESTIMATES           (APPROX. ST. DEV.)    T VALUE
1  ALPHA               0.190378       (0.2203E-01)          8.6
2  A                   0.613290E-02   (0.3495E-03)          18.
3  B                   0.105271E-01   (0.8027E-03)          13.

RESIDUAL    STANDARD DEVIATION =         3.3616721630
RESIDUAL    DEGREES OF FREEDOM =         211
REPLICATION STANDARD DEVIATION =         3.2817625999
REPLICATION DEGREES OF FREEDOM =         192
LACK OF FIT F RATIO =       1.5474 = THE  92.6461% POINT OF THE
F DISTRIBUTION WITH     19 AND    192 DEGREES OF FREEDOM

COEF AND SD(COEF) WRITTEN TO FILE DPST1F.DAT
```
Plot of Predicted Values with Raw Data
Run Sequence Plot of Residuals
Normal Probability Plot of Residuals

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Date created: 06/05/2001
Last updated: 09/28/2016